On the Pareto optimum sensitivity analysis in multicriteria optimization

To analyse the trade-o relations among the set of criteria in multicriteria optimization, Pareto optimum sensitivity analysis is systematically studied in this paper. Original contributions cover two parts: theoretical demonstrations are rstly made to validate the gradient projection method in Pareto optimum sensitivity analysis. It is shown that the projected gradient direction evaluated at a given Pareto optimum in the design variable space rigorously corresponds to the tangent direction of the Pareto curve=surface at that point in the objective space. This statement holds even for the change of the set of active constraints in the perturbed problem. Secondly, a new active constraint updating strategy is proposed, which permits the identi cation of the active constraint set change, to determine the in uence of this change upon the di erentiability of the Pareto curve and nally to compute directional derivatives in non-di erentiable cases. This work will highlight some basic issues in multicriteria optimization. Some numerical problems are solved to illustrate these novelties